Update Gemini template [Go Web App] to new SDK

## Current template:
https://studio.firebase.google.com/new/gemini

### Template Options:
Environment: Go Web App
Use LangChain: False

## Updates Needed

- [ ] Migrate generative AI SDK to the new [Go SDK](https://pkg.go.dev/google.golang.org/genai)
- [ ] Update any code examples and README

Start from the Go Web App template at https://studio.firebase.google.com/new/gemini and inspect its current generative AI SDK usage and README. Compare the implementation with the google.golang.org/genai Go SDK documentation, update the code examples and README, and verify that the template still works with the new SDK.

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